Difference of Convex Algorithm for Warm-Start Quantum Approximate Optimization Algorithm

The Quantum Approximate Optimization Algorithm (QAOA) stands as a hybrid classical-quantum algorithm utilized for addressing combinatorial optimization challenges. Central to its effectiveness is the initial mixer, which is responsible for instigating the optimization process by generating the starting state. However, conventional QAOA implementations often assign equal probabilities to all solutions at the outset, potentially resulting in suboptimal performance when tackling complex combinatorial optimization problems. In this study, a novel enhancement is proposed to the QAOA, leveraging the Difference of Convex Algorithm (DCA). This method aims to refine QAOA's performance by facilitating the discovery of optimal parameters through a continuous warm-start approach, as originally introduced by Egger et al. Through experimentation utilizing datasets from prior studies focusing on the weighted maximum cut problem, the efficacy of our proposed method is evaluated. Comparative analysis against existing methodologies reveals a significant improvement in the approximate ratio achieved by our approach.